Titlebook: Quaternion and Clifford Fourier Transforms and Wavelets; Eckhard Hitzer,Stephen J. Sangwine Book 2013 Springer Basel 2013 complex numbers.

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Bochner’s Theorems in the Framework of Quaternion Analysiser–Stieltjes integral .. The purpose of this chapter is to give a characterization of the class . and to give a generalization of the classical theorem of Bochner in the framework of quaternion analysis.

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Bochner–Minlos Theorem and Quaternion Fourier TransformThe first part of this chapter features certain properties of the asymptotic behaviour of the quaternion Fourier transform. In the second part we introduce the quaternion Fourier transform of a probability measure, and we establish some of its basic properties. In the final analysis, we introduce th

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Square Roots of –1 in Real Clifford Algebras1. This extends to a geometric interpretation of quaternions as the side face bivectors of a unit cube. Systematic research has been done [33] on the biquaternion roots of –1, abandoning the restriction to blades. Biquaternions are isomorphic to the Clifford (geometric) algebra .. of ?.. Further res

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A General Geometric Fourier Transformition of a general geometric Fourier transform covering most versions in the literature. We show which constraints are additionally necessary to obtain certain features such as linearity or a shift theorem. As a result, we provide guidelines for the target-oriented design of yet unconsidered transfo

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Clifford–Fourier Transform and Spinor Representation of Imageshe usual Weierstrass representation of minimal surfaces (., surfaces with constant mean curvature equal to zero) to arbitrary surfaces (immersed in .). We investigate applications to image processing focusing on segmentation and Clifford–Fourier analysis. All these applications involve sections of t

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Generalized Analytic Signals in Image Processing: Comparison, Theory and Applicationslications to and of their comparison on artificial and real-world image samples..We first start by reviewing the basic concepts behind analytic signal theory and derive its mathematical background based on boundary value problems of one-dimensional analytic functions. Following that, two generalizat

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A Generalized Windowed Fourier Transform in Real Clifford Algebra ,,first introduced from the mathematical aspect by Brackx. In this chapter, we propose the Clifford windowed Fourier transform using the kernel of the CFT. Some important properties of the transform are investigated.